The France international struck first in the 60th minute when he finished off a sublime low cross from Didier Drogba as Chelsea defied their critics with a performance of grit and quality.
Substitute Malouda sealed the win in injury-time when he slid home another low cross from Drogba.
Nic of time: Anelka nips in front of Carragher to break the deadlock
Carlo Ancelotti's side were desperate to get back to winning ways in the league after their 3-1 drubbing by Wigan last week and a lacklustre victory over Apoel Nicosia in the Champions League in midweek.
But it was Liverpool who had the best of the early exchanges and the game sparked into life in the 12th minute when Fernando Torres was fortunate not to receive a yellow card for a late challenge on Chelsea captain John Terry.
The Spaniard's right foot was clearly too high and raked the shins of the England defender. However, referee Martin Atkinson opted to give the Liverpool striker a lengthy lecture, much to the annoyance of the home fans.
Liverpool continued to dominate but a shot from Albert Riera was high and wide of the target in the 19th minute. Michael Essien appeared to be late and high with a challenge on Javier Mascherano but referee Atkinson was perfectly positioned to see the incident and ignored Chelsea appeals.
The Liverpool player soon rose to his feet without any damage to his right leg. Both sides were full of attacking desire but neither goalkeeper had been tested at the midway stage of the opening half.
Frustration: Torres finds his way to goal blocked by Ivanovic and Carvalho
Liverpool's Jose Reina finally collected a header from Drogba just beneath the crossbar in the 24th minute but Chelsea's threat was somewhat impotent.
In the 27th minute Reina was called into action again when Essien's cross was met by Anelka. The France international was unmarked but despite the luxury of a free header, he could not find a way past the Liverpool goalkeeper.
Liverpool were handed a chance to open the scoring in the 29th minute when Branislav Ivanovic was adjudged to have brought down Torres.
The free-kick was some 25 yards out but Gerrard's effort sailed over the crossbar to the delight of the home fans. Four minutes later Chelsea squandered a chance of their own after Drogba had been brought down by Jamie Carragher near the corner flag. Deco's free-kick into the penalty area was well placed but Michael Ballack's header was off target from six yards.
Chelsea were now enjoying their best spell of the game and when Lampard's 38th-minute corner fell to Essien at the far post, the Ghanaian international forced Reina to make a save at the second attempt.
Liverpool responded with Dirk Kuyt crossing for Torres to head straight at Hilario from six yards.
It's over: Malouda (grounded) sees the ball go in despite the efforts of Johnson
Deco was booked for a foul on Kuyt in the 44th minute and Riera forced Hilario into a late save with a 40-yard low drive.
In the 57th minute Liverpool won a free-kick when Riera was blocked by Ballack - but Gerrard's delivery was met by a confident punch from Hilario and Chelsea survived a difficult moment.
The Blues broke the deadlock on the hour after Mascherano lost possession to Lampard in the Chelsea half.
Essien and Deco fed the ball wide to Drogba on the left - and his centre was perfect for Anelka to convert his fifth goal of the season.
In the 63rd minute, Drogba met Lampard's free-kick but his header was well held by Reina - and four minutes later the visitors replaced Riera with Yossi Benayoun.
In the 77th minute Chelsea won a free-kick in a dangerous area when Lampard was brought down by Gerrard.
The challenge earned Gerrard a yellow card and Chelsea almost went two goals in front but Drogba was just wide of the right-hand post with his free-kick. Chelsea's goal was now under siege and Torres wasted a glorious chance to level the scores when he shot wide in the 80th minute.
Substitute Malouda then settled the outcome when he slid the ball home from close range in injury-time.
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